I am kind of getting in too many details here, but I used to live there for over seven years, and this is a good question for me.
One thing that I forgot to mention is Sam's Club. You definitely want to sign up and shop there. There is a good Smart & Final close to Decatur and Charleston, I would recommend checking it out too. I've seen another one that was very bad, and these are the only two that I've seen. In the good one they had a lot of good products, like frozen chicken wings, and other things that one person was buying, and selling in his restaurant.
Sam's Club + (Costco) + (Smart & Final) + Food 4 Less + 99 Cent store (or / and Dollar Tree) is where you want to shop, I would say. Sam's Club is very good, and the prices are low too.
You can get a whole roasted chicken (warmed up and ready to eat) for as low as $2.00 (they lower the prices at the end of the day, if food does not sale) in Walmart Neighborhood Market. This one is generally more expensive, so I would not shop there, but chicken is very good.
You can check out
H&H Hawaiian BBQ, for a change too. This one is not as good as the other places that I've mentioned so far, from my point of view.